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Henrique Consoni
Henrique Consoni

Patrick Morandi Field Galois Theory Solutions


Patrick Morandi Field and Galois Theory Solutions




Field and Galois theory is a branch of abstract algebra that studies the properties of fields and their extensions, especially those related to the solvability of polynomial equations by radicals. One of the main goals of field and Galois theory is to determine which polynomials are solvable by radicals, and to describe the structure of the Galois group of a polynomial, which is a group that measures the symmetry of its roots.


Patrick Morandi is a professor of mathematics at the University of New Mexico, who has written a textbook on field and Galois theory. The book covers topics such as finite fields, algebraic extensions, splitting fields, separability, normality, algebraic closure, transcendence degree, infinite Galois extensions, solvability by radicals, cyclotomic extensions, Kummer theory, and more. The book is intended for graduate students and advanced undergraduates who have some background in abstract algebra.




patrick morandi field galois theory solutions



The book contains many exercises that help the reader to understand and apply the concepts and results of field and Galois theory. However, the book does not provide solutions to the exercises, which can be frustrating for some students who want to check their work or learn from their mistakes. Fortunately, there are some online resources that offer solutions to some or all of the exercises in Morandi's book.


Online Resources for Solutions





  • : This website provides solutions to exercises in various textbooks, including Morandi's Field and Galois Theory. The solutions are uploaded by students or teachers who have used the book. The quality and completeness of the solutions may vary, but they can be useful as a reference or a guide.



  • : This is a question-and-answer website for mathematics enthusiasts of all levels. Users can ask or answer questions about any topic in mathematics, including field and Galois theory. Some questions are related to specific exercises in Morandi's book, and some users have provided detailed solutions or hints to these exercises. The answers are usually well-written and verified by other users.



  • : This is the official website of Springer, the publisher of Morandi's book. Users who have access to SpringerLink can download or read the book online. The website also provides some supplementary materials for the book, such as errata, reviews, and related books.




Conclusion




Patrick Morandi's Field and Galois Theory is a comprehensive and rigorous textbook that covers many topics in field and Galois theory. The book has many exercises that help the reader to practice and master the subject. However, the book does not provide solutions to the exercises, which can be challenging for some students. Fortunately, there are some online resources that offer solutions to some or all of the exercises in Morandi's book. These resources can be helpful for students who want to learn from their own work or from others' work.


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